Nick Clegg and David Cameron at the state opening of parliament. Photograph: Facundo Arrizabalaga/EPA

Liberal Democrat cabinet members are pressing for a referendum on voting reform for the election of MPs to be held next May, seeing it as the best chance of winning public backing for one of Nick Clegg's main political projects.

The Lib Dems fear a delayed referendum would lead voters to reject change and punish an unpopular coalition government in the wake of a programme of big spending cuts.

Clegg, the deputy prime minister, had at one time been looking at a date as early as this October but there is little prospect of the parliamentary reform bill, announced in today's Queen's speech, reaching the statute book in time.

A referendum on 5 May 2011 could also boost turnout since nearly 12 million voters will be going to the polls in elections for the Scottish parliament, Welsh assembly and about 280 English local councils.

But a referendum has the potential to disrupt the coalition since David Cameron and almost the entire Conservative party oppose voting reform.

The prime minister gave no hint today on when the referendum on the alternative vote system (AV) would be held.

Pro-AV Cabinet members said today that they regarded May 2011 as probably the optimum date, but said the issue was extremely delicate since Cameron and Clegg would be campaigning on different sides during the referendum, which will offer a choice between the existing first- past-the-post system and AV.

Advocates of the reform fear that if the coalition government is unpopular at the time of the referendum, support for AV will suffer since campaigners against AV will argue the reform would lead to more hung parliaments.

Peter Lilley, a former Tory cabinet minister, used his speech opening the debate on the Queen's speech to warn against AV saying it would lead to "permanent hung parliaments".

Clegg is due to hold his first talks on the issue with the justice secretary, Ken Clarke, tomorrow, and has already been holding discussions within government on the referendum's timing.

Some Lib Dems point out that by next May an unpopular cuts programme will not have started in earnest, and by contrast the linking of pensions to earnings will have just been implemented. They also hope a budget will have just taken hundreds of thousands out of the tax system by reforms to the personal allowance system.

The Conservatives said today that the bill on AV would also contain measures to reduce the number of constituencies by as much as 10% and to equalise their size – a complex, controversial and time-consuming measure that will benefit the Tories.

The Lib Dems say the referendum can be held before the boundary review is complete as long as the legislation has been passed setting the constituency boundary review in train. But some senior Conservative sources were hinting the boundary review would have to be under way before the AV referendum could be staged, so delaying its date.

Tory sources were also emphasising that if the referendum rejected a change to the voting system, changes to constituency boundaries would still be implemented, a move likely to make it easier for their party to be re-elected.

Amid all the pomp of the state opening of parliament, held against the backdrop of coming spending cuts, a tougher welfare regime and tax rises, the Cameron government announced 23 bills and one draft bill, many of them dismantling what the prime minister described as "the top-down apparatus of state control".

He promised his government marked "an end to the years of recklessness and big government and the beginning of the years of responsibility and good government".

The prime minister said Labour had left Britain in an appalling mess with a deficit bigger than Greece's. "Until they learn what they got so badly wrong I am not sure whether the public are going to listen to them again," he said in his speech to the Commons.

The coalition government promised a lightning start to its legislative programme, with a brief but all-important bill published tomorrow to spread academy schools across the secondary and primary sectors.

On Thursday the home secretary, Theresa May, will publish a bill to abolish ID cards and the national identity register, a precursor to a grandly titled freedom (great repeal) bill, designed to protect privacy, extend freedom of information and review anti-terrorism legislation.

Other bills will also part-privatise the Royal Mail, put an annual cap on non-EU migrants in the tens of thousands, allow for elected police commissioners, and remove barriers to new providers setting up schools within the state system. Ministers are still working on the details of proposed citizens' referendums on local government issues.

There were also signs tonight that Cameron would back down over aspects of his plan for a five-year fixed-term parliament, by saying that the proposed majority of 55% required before a parliament could be dissolved early would only apply to a move by the prime minister to dissolve parliament early. A simple majority would still be required for a government to lose a confidence motion.